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Modern theory of the orbital magnetization is applied to the series ofinsulating perovskite transition metal oxides (orthorhombic YTiO$_3$,LaMnO$_3$, and YVO$_3$, as well as monoclinic YVO$_3$), carrying a netferromagnetic (FM) moment in the ground state. For these purposes, we use aneffective Hubbard-type model, derived from the first-principleselectronic-structure calculations and describing the behavior of magneticallyactive states near the Fermi level. The solution of this model in themean-field Hartree-Fock approximation with the relativistic spin-orbit couplingtypically gives us a distribution of the local orbital magnetic moments, whichare related to the site-diagonal part of the density matrix $\hat{\cal D}$ bythe "standard" expression $\boldsymbol{\mu}^0 = - \mu_{\rm B} \mathrm{Tr} \{\hat{\textbf{L}} \hat{\cal D} \}$ and which are usually well quenched by thecrystal field. In this work, we evaluate "itinerant" corrections $\Delta\boldsymbol{\cal M}$ to the net FM moment, suggested by the modern theory. Weshow that these corrections are small and in most cases can be neglected.Nevertheless, the most interesting aspect of our analysis is that, even forthese compounds, which are typically regarded as normal Mott insulators, the"itinerant" corrections reveal a strong $\textbf{k}$-dependence in thereciprocal space, following the behavior of Chern invariants. Therefore, thesmall value of $\Delta \boldsymbol{\cal M}$ is the result of strong cancelationof relatively large contributions, coming from different parts of the Brillouinzone. We discuss details as well as possible implications of this cancelation,which depends on the crystal structure as well as the type of the magneticground state.

Orbital magnetization of insulating perovskite transition-metal oxides with the net ferromagnetic moment in the ground state